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Solve for x. Enter the solutions from least to greatest. {:[x^(2)-2x-35=0],[" lesser "x=◻],[" greater "x=◻]:}

Solve for x x . Enter the solutions from least to greatest.\newlinex2−2x−35=0 lesser x=□ greater x=□ \begin{array}{l} x^{2}-2 x-35=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}

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Q. Solve for x x . Enter the solutions from least to greatest.\newlinex2−2x−35=0 lesser x=□ greater x=□ \begin{array}{l} x^{2}-2 x-35=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}
  1. Identify the quadratic equation: Identify the quadratic equation to solve.\newlineThe given quadratic equation is x2−2x−35=0x^2 - 2x - 35 = 0. We need to find two numbers that multiply to −35-35 and add up to −2-2.
  2. Factor the quadratic equation: Factor the quadratic equation.\newlineThe two numbers that multiply to −35-35 and add up to −2-2 are −7-7 and 55. Therefore, we can factor the equation as follows:\newline(x−7)(x+5)=0(x - 7)(x + 5) = 0
  3. Solve for x by setting each factor equal to zero: Solve for x by setting each factor equal to zero.\newlineFirst, set the first factor equal to zero:\newlinex−7=0x - 7 = 0\newlineAdd 77 to both sides to solve for x:\newlinex=7x = 7
  4. Solve for x using the second factor: Solve for x using the second factor.\newlineNow, set the second factor equal to zero:\newlinex+5=0x + 5 = 0\newlineSubtract 55 from both sides to solve for x:\newlinex=−5x = -5
  5. Write the solutions in ascending order: Write the solutions in ascending order.\newlineThe solutions are x=−5x = -5 and x=7x = 7. In ascending order, the lesser value is −5-5 and the greater value is 77.

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